ALGEBRA 2
5.5: Complex Numbers & Roots
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Imaginary Numbers
Invented to solve quadratics that have no zeros
What happens when we have the square root of a negative
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1) 4
2) 32
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1) x2 = -144
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5)2i 3i
3)  25
6) 2 32
Solve Simple Quadratics with Imaginary Numbers
2) 5x2 + 90 = 0
Complex Numbers
a + bi
o a is the _________________
o b is the ________________
When b = 0, _____________
When a = 0, _____________
a+bi = c+di, when _______________________
Computations with complex #’s
o Treat i just like a _______________
o Remember ___________
1) (4 + 3i) + (7 + 8i)
Examples
2) (4 + 2i) (3 – 5i)
3) Find the values of x and y that make the equation 4x + 10i = 2 – (4y)i true.
4)2 24
Find complex zeros using complete the square.
1) f(x) = x + 10x + 26
2) g(x) = 3x2 + 12x + 36
2
Complex Conjugates
 Real parts are the _______and the imaginary parts are ______________________
 ____________________________
 This is what occurs when the roots are complex (previous slide)
 Example: Find each complex conjugate
1) 8 + 5i
2) 6i
Assignment #5: Page 353 #’s 18-36,(96)